We study the partition function of the matrix model of finite size that
realizes the irregular conformal block for the case of the
supersymmetric gauge theory with . This model has been obtained
in [arXiv:1008.1861 [he...

We argue that the level-1 elliptic algebra Uq,p(gˆ) is a dynamical symmetry realized as a part of 2d/5d correspondence where the Drinfeld currents are the screening currents to the q-Virasoro/W block in the 2d side. For the case of Uq,p(slˆ(2)), t...

International Journal of Modern Physics A 32(11) 1750056 [23 pages] Apr 2017 [Refereed]

A set of Schwinger-Dyson equations forming constraints for at most three resolvent functions are considered for a class of Chern-Simons matter matrix models with two nodes labelled by a non-vanishing number n. The two cases n=2 and n=−2 label resp...

The five-dimensional AGT correspondence implies the connection between the q-deformed Virasoro block and the 5d Nekrasov partition function. In this paper, we determine a q-deformation of the four-point block in the Coulomb gas representation from...

We demonstrate that the parafermions appear in the r-th root of unity limit of q-Virasoro/W(n) algebra. The proper value of the central charge of the coset model slˆ(n)r⊕slˆ(n)_{m-n}/slˆ(n)_{m−n+r} is given from the parafermion construction of the...

We propose and demonstrate a limiting procedure in which, starting from the
q-lifted version (or K-theoretic five dimensional version) of the (W)AGT
conjecture to be assumed in this paper, the Virasoro/W block is generated in
the r-th root of unit...

We introduce An(1) (n=1,2,...) affine quiver matrix model by simply adopting
the extended Cartan matrices as incidence matrices and study its finite N
Schwinger-Dyson equations as well as their planar limit. In the case of n=1, we
extend our analy...

We observe that, at beta-deformed matrix models for the four-point conformal
block, the point q=0 is the point where the three-Penner type model becomes a
pair of decoupled two-Penner type models and where, in the planar limit, (an
array of) two-c...

Misc

We propose a limiting procedure in which, starting from the q-lifted version
(or K-theoretic five dimensional version) of the (W)AGT conjecture to be assumed,
the Virasoro/W block is generated in the r-th root of unity limit in q in the 2d side,...

The -deformed matrix models of Selberg type are introduced. They are exactly calculable by using the Macdonald-Kadell formula. With an appropriate choice of the integration contours and interactions, the partition function of the matrix mod...

The two-dimensional Ising model has been studied since the work of Onsager. It is well-known that this model is equivalent to a free fermion field theory. Because of this property, some correlation functions can be written in terms of the determin...